## Goal

Wave agitation studies in harbors are an important requirement for control and design. However, they involve an exhaustive demand of computer costs, mainly due to these two factors:

- Incoming waves of design spread out in large ranges of frequencies and directions. In practice, this implies thousands of different computations trying to cover a realistic incoming wave spectrum.
- Each single computation (i.e. fixed incoming frequency and direction) involves several numerical challenges to be considered. More precisely: large 2D domains with small geometric details that are influential in the solution, artificial boundary conditions, and dispersion error for higher frequencies.

Our main goal is to develop a novel methodology dealing with these two previous issues, providing extremely fast solutions for any value of the incoming wave parameters, and using negligible computational resources.

## Strategy and results

We use an a priori model order reduction (MOR) technique, called Proper Generalized Decomposition (PGD), to *offline* approximate the generalized 4D solution of an elliptic harbor model. The augmented dimensionality of the original 2D problem comes from considering both, the incoming wave direction and frequency, as new 1D coordinates of the problem. Thus, the original harbor model is parameterized. In the *online* phase, the PGD provides a real-time solution to the original problem at any incoming parameter value (within a range of interest).

Application to the Barcelona harbor is depicted in the figure above. This harbor presents a size of 12 km long, and its agitation remains in the mid-high frequency range for a realistic wave spectum of the area. The 4D online PGD solution (second row in the figure) is immediately evaluated for each required parameter (see each column in the figure), and it presents sufficient accuracy compared to standard 2D fourth-order FEM computations.

Developed by:

David Modesto

Sergio Zlotnik

Antonio Huerta

More information at this link.